This is a very old argument; here we look at the best version of it, provided by Samuel Clarke, a contemporary of Newton.

1) Nothing cannot cause anything.
2) Something exists now.
3) There is a cause or reason for everything
NOTE: this is called the Principle of Sufficient Reason
4) Hence, at no time there was nothing, i.e., something has been in existence from eternity.
5) This something is either:
      a) an independent being, i.e., a being which has within itself the reason of its own existence (i.e., God)
     or
     b) an infinite chain of dependent beings.
Now Clarke tries by a reductio to show that (5b) is false.
6) suppose (5b) is the case.
7) since each member of the infinite chain is a dependent being, it follows that no cause can be given for the existence of the series itself since:
     a) nothing exists outside the infinite series to cause it  (hypothesis (5b))
     and
     b) nothing in the infinite series is the cause of the series but at most  a cause only of what comes after it.
8) hence, the series exists without cause or reason, which is impossible.
9) Hence (5b) is false.
10) hence, (5a) must be the case, i.e., there exists from eternity an independent being, i.e. God.

NOTES:
i)The series over and above its members does not exist in reality; it is just a concept.  Hence, when each member is accounted for, no further question can be asked (example of the 20 particles).  Hence, Clarke has no reason to look for the cause of the infinite series each of which members is acounted for.
Perhaps Clarke is really asking why there is something rather than nothing: although each member of the series is accounted for, there is no cause for why there is something (the series) rather than nothing.
ii) the divine being exists necessarily but is not self-caused.
iii) The argument does not intend to prove that the world is not eternal: being eternal is one thing; existing necessarily is another.